The analysis by Shapiro et al. (1969) of a two-dimensional peristaltic pump at small Reynolds number and with long wavelengths is extended to include a Newtonian peripheral layer adjacent to the wall to simulate the effect of a coating in physiological flows. An earlier analysis by Shukla et al. (1980) violates mass conservation because of an incorrect deduction of the interface shape. We present a detailed analysis of the effect of the peripheral layer on the fluid motions, the pumping characteristics, and the phenomena of reflux and trapping. For prescribed wall motion, a peripheral layer more viscous than the inner fluid improves pumping performance, while a less-viscous outer layer degrades performance. Even a very thin peripheral layer may substantially reduce pumping if the viscosity in this layer is very low relative to the inner region. The effects of the peripheral layer on reflux and trapping depend on the conditions which are held fixed while making the comparison. However, the general trend with decreasing peripheral-layer viscosity is towards an overall decrease in trapping, a decrease in reflux with fixed total volume flow rate, but an increase in reflux with fixed pressure head.

A workshop was held at MIT in February 1986 for specialists performing theoretical research on the interactions of water waves with floating or submerged bodies. The principal applications of this field are related to ship hydrodynamics and to wave loadings on offshore platform. In addition to the traditional approach based on linearization of the wave and body motions, substantial progress has been made on nonlinear problems including both analytical and numerical studies. Subsequent workshops are planned on an annual basis.

Burst structures in the near wall region of turbulent flows are associated with a large portion of the turbulent momentum transport from the wall. However, quantitative measures of the timescales associated with the burst event are not well defined, largely due to ambiguities associated with the methods used to detect a burst.

In the present study, Eulerian burst-detection schemes were developed through extensions of the uv quadrant 2, VITA, and u-level techniques. Each of the basic techniques detects ejections. One or more ejections are contained in each burst and hence the key idea is to identify and to group those ejections from a single burst into a single-burst detection. When the ejection detections were grouped appropriately into burst detections, all of the extended techniques yielded the same average time between bursts as deduced from flow visualization for fully-developed channel flow in the range 8700 [les ] Reh [les ] 17 800. The present results show that inner variables (wall shear stress and kinematic viscosity) are the best candidates for the proper scaling of the average time between bursts. Conditional velocity sampling during burst and ejection detections shows that these burst events are closely correlated with slower-than-average moving fluid, moving both away from the wall and toward the wall.

The main goal of this paper is to clarify the spatial instability of a piecewise linear free shear flow. We do this by obtaining numerical solutions to the Orr–Sommerfeld equation at high Reynolds numbers. The velocity profile chosen is very much like a piecewise linear one, with the exception that the corners have been rounded so that the entire profile is infinitely differentiable. We find that the (viscous) spatial instability of this modified profile is virtually identical to the inviscid spatial instability of the piecewise linear profile and agrees qualitatively with the inviscid results for the tanh profile when the shear layers are convectively unstable. The unphysical features, previously identified for the piecewise linear velocity profile, arise only when the flow is absolutely unstable. In a nutshell, we see nothing wrong with the inviscid spatial instability of piecewise linear shear flows.